Put the egg whites and sugar in a heatproof bowl over a pan of simmering water.
Stir together gently over the heat using a whisk until all the grains of sugar have dissolved (check by rubbing some between your fingers).
Transfer to a large bowl or the bowl of a free-standing mixer and, using a balloon whisk, whisk for a minimum of 10 minutes, until the mixture has reached a cool room temperature.
With the whisk still going quite fast, start adding the butter in small chunks, bit-by-bit, until all the butter is in.
If it seems very sloppy, turn the speed up and keep whisking! If things are getting very hot, put the mixture into the fridge for a few minutes before resuming.
Finally, add the Baileys Original Irish Cream whilst whisking, and mix until smooth and tasty. Don’t be tempted to put more Baileys Original Irish Cream in as it has a tendency to split with too much liquid!